Cross-polarized linear antenna array will be widely employed in LTE systems. The cross-polarized linear antenna array can be considered as two groups of coplanar polarized antennas, antennas in each group being on the same polarization.
The channel characteristics of the cross-polarized linear antenna array are illustrated in the following. The channel h of the cross-polarized linear antenna array can be represented by:
  h  =      (                                        h            1                                                            h            2                                )  
where h1 represents a sub-channel of the first group of antennas on one polarization and h2 represents a sub-channel of the second group of antennas on the other polarization.
From the following documents, straightforwardly, in the case of no scattering, there exists a complex scaling factor between h1 and h2,
            β      ′        ⁢          ⅇ              j        ⁢                                  ⁢                  δ          ′                      =            h      2              h      1      
with β denoting the modulus and δ denoting the phase.
Documents:
L. Jiang, L. Thiele, and V. Jungnickel, “On the Modelling of Polarized MIMO Channel,” 13th European Wireless Conference, Paris, France, April 2007.
L. Jiang, L. Thiele, and V. Jungnickel, “Polarization Rotation Evaluation for Macrocell MIMO Channel,” in Proc. IEEE ISWCS, Italy, September 2009.
Efficient feedback codebooks and precoders are required to do single user or multi-user precoding with cross-polarized linear antenna array.
Currently, discussions in 3GPP on LTE-A, various feedback schemes have been proposed for cross-polarized linear antenna array. In R1-103026, “Views on the feedback framework for Rel 10”, Samsung, 3GPP TSG RAN1 WG1 61 and R1-101742, “Further refinements of feedback framework”, Ericsson, 3GPP TSG RAN1 WG1 60b, the generated precoder matrix F is in the form of co-phasing:
                    F        =                  (                                                                      f                  1                  ′                                                            …                                                              f                  L                  ′                                                                                                                          ⅇ                                          j                      ⁢                                                                                          ⁢                                              δ                        1                        ′                                                                              ⁢                                      f                    1                    ′                                                                              …                                                                                  ⅇ                                          j                      ⁢                                                                                          ⁢                                              δ                        L                        ′                                                                              ⁢                                      f                    L                    ′                                                                                )                                    (        1        )            
wherein F is a precoding matrix of size M′×L′ with the number of antennas and L′ the number of data stream layers, (f′1 . . . f′L) is the upper sub-matrix of F of size M′/2×L′ representing the precoding matrix for the first group of antennas and (ejδ′1f′1 . . . ejδ′Lf′L) is the lower sub-matrix of F of size M′/2×L′ representing the precoding matrix for the second group of antennas with δ′1, . . . , δ′L a non-negative real number.
However, the form of precoder in equation (1) does not fully match the channel characteristics with cross-polarized linear antenna array. System performance can be further improved by designing better feedback codebook to match the channel characteristics.
Therefore, though various feedback schemes have been proposed, the current schemes cannot fully match channel characteristics of cross-polarized linear antenna array and thus cannot work efficiently.